how many different words can be formed of the letters of the word malenkov so that no two vowels are together?
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First part: we shall arrange the consonants that is m l n k v = 5!
Second part:
Now we shall insert vowels in between like this _m_l_n_k_v_
6 places and we have to put three vowels between them, So we first pick 3 place out of these 6 => =6!3!(6−3)!=6!3!(6−3)! = 2020
Third part:
Arrange the 3 vowels that is 3!3! ways
---------Doing the calculations finally------------
5!∗20∗3!
1440
Second part:
Now we shall insert vowels in between like this _m_l_n_k_v_
6 places and we have to put three vowels between them, So we first pick 3 place out of these 6 => =6!3!(6−3)!=6!3!(6−3)! = 2020
Third part:
Arrange the 3 vowels that is 3!3! ways
---------Doing the calculations finally------------
5!∗20∗3!
1440
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